# Graph f(x)=x^2-3x-2

Graph f(x)=x^2-3x-2
Find the properties of the given parabola.
Rewrite the equation in vertex form.
Complete the square for .
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Multiply by .
Find the value of using the formula .
Simplify each term.
Raise to the power of .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Substitute the values of , , and into the vertex form .
Set equal to the new right side.
Use the vertex form, , to determine the values of , , and .
Since the value of is positive, the parabola opens up.
Opens Up
Find the vertex .
Find , the distance from the vertex to the focus.
Find the distance from the vertex to a focus of the parabola by using the following formula.
Substitute the value of into the formula.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Find the focus.
The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.
Substitute the known values of , , and into the formula and simplify.
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
Find the directrix.
The directrix of a parabola is the horizontal line found by subtracting from the y-coordinate of the vertex if the parabola opens up or down.
Substitute the known values of and into the formula and simplify.
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Select a few values, and plug them into the equation to find the corresponding values. The values should be selected around the vertex.
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
One to any power is one.
Multiply by .
Simplify by subtracting numbers.
Subtract from .
Subtract from .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Raising to any positive power yields .
Multiply by .
Subtract from .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Raise to the power of .
Multiply by .
Simplify by subtracting numbers.
Subtract from .
Subtract from .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Raise to the power of .
Multiply by .
Simplify by subtracting numbers.
Subtract from .
Subtract from .
The value at is .
Graph the parabola using its properties and the selected points.
Graph the parabola using its properties and the selected points.
Direction: Opens Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
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### Name

Name seven hundred sixty-six million four hundred thirty thousand four hundred four

### Interesting facts

• 766430404 has 16 divisors, whose sum is 1725221268
• The reverse of 766430404 is 404034667
• Previous prime number is 2357

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 34
• Digital Root 7

### Name

Name one billion three hundred forty-six million three hundred twenty-six thousand six hundred sixty-eight

### Interesting facts

• 1346326668 has 32 divisors, whose sum is 3371029920
• The reverse of 1346326668 is 8666236431
• Previous prime number is 653

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 45
• Digital Root 9

### Name

Name one billion eight hundred sixty-three million one hundred thirty-seven thousand three hundred fourteen

### Interesting facts

• 1863137314 has 8 divisors, whose sum is 2795724288
• The reverse of 1863137314 is 4137313681
• Previous prime number is 2767

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 37
• Digital Root 1